A248091 Expansion of x^3*(1-2x-x^2-x^3+x^4+x^5)/((1+x)*(1-3x+x^2-x^3+3x^4)).

0, 0, 0, 1, 0, 1, 1, 3, 6, 16, 39, 101, 259, 670, 1732, 4485, 11613, 30079, 77910, 201812, 522763, 1354153, 3507775, 9086502, 23537592, 60971593, 157940361, 409127579, 1059801190, 2745301576, 7111410031, 18421346973

Offset: 0

Author

Emeric Deutsch, Oct 28 2014

Keywords

• nonn

Comments

a(n) = number of nonisomorphic n-element posets P such that if 1<=i<=n-1, then P has exactly 3 order ideals of cardinality i.

References

• R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 1, 2nd ed., 2012, Exercise 3.35c, p. 359.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,2,0,-2,-3).

Programs

Maple

g := x^3*(x^5+x^4-x^3-x^2-2*x+1)/((x+1)*(3*x^4-x^3+x^2-3*x+1)): gser := series(g, x = 0, 45): seq(coeff(gser, x, n), n = 0 .. 40);

Mathematica

CoefficientList[Series[x^3*(1 - 2 x - x^2 - x^3 + x^4 + x^5)/((1 + x) (1 - 3 x + x^2 - x^3 + 3 x^4)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Oct 28 2014 *)